MATCDF

MATCDF (LET)

Library Function

Compute the classical matching cumulative distribution function.

The classical matching distribution has the following probability mass function:

with k a non-negative integer denoting the number of items parameter.

The cumulative distribution function is computed by summing the probability density function.

LET <y> = MATCDF(<x>,<k>)             <SUBSET/EXCEPT/FOR qualification>
where <x> is a variable, a number, or a parameter containing values between 0 and <k>;
            <k> is a number or parameter that defines the upper limit of the matching distribution;
            <y> is a variable or a parameter (depending on what <x> is) where the computed cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = MATCDF(3,20)
LET Y = MATCDF(X,100)

For sufficiently large values of k, the classical matching distribution can be accurately approximated with a Poisson distribution with = 1. Dataplot computes MATCDF from the above definition for values of k < 20. For values of k ≥ 20, Dataplot computes MATCDF using the Poisson cdf with = 1.

None

None

MATPDF	= Compute the matching probability mass function.
MATPPF	= Compute the matching percent point function.
POIPDF	= Compute the Poisson probability mass function.
LCTPDF	= Compute the leads in coin tossing probability mass function.
DISPDF	= Compute the discrete uniform probability mass function.
LOSPDF	= Compute the lost games probability mass function.
ARSPDF	= Compute the arcsine probability density function.
BETPDF	= Compute the beta probability density function.
UNIPDF	= Compute the uniform probability mass function.

Johnson, Kotz, and Kemp (1992), "Univariate Discrete Distributions", Second Edition, Wiley, pp. 409-410.

Distributional Modeling

2006/6

 
TITLE CASE ASIS
TITLE Matching Cumulative Distribution Function CR() ...
      (N = 50)
LABEL CASE ASIS
Y1LABEL Probability
X1LABEL X
LINE BLANK
SPIKE ON
TIC OFFSET UNITS SCREEN
TIC OFFSET 3 3
PLOT MATCDF(X,50) FOR X = 0 1 50